Density model checks via the lack-of-fitness

Valentin Patilea () and François Portier ()
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Valentin Patilea: Univ Rennes, Ensai
François Portier: Univ Rennes, Ensai

Statistical Papers, 2025, vol. 66, issue 2, No 1, 26 pages

Abstract: Abstract Parametric multivariate density estimators, such as the maximum likelihood, can be generalized by mixing them with a kernel estimator. The mixture weights can be chosen to optimize a measure of the goodness-of-fit. The optimal weight of the kernel estimator, which we call the lack-of-fitness coefficient, then provides a simple check of the parametric model. The test statistic is defined as the appropriately normalized lack-of-fitness coefficient. When the parametric density model is correct, the statistic converges in distribution to the positive part of a standard Gaussian variable, regardless of the dimension of the observations. In addition, the test has good power against alternative hypotheses approaching the density model.

Keywords: Central limit theorem; Concavity; Leave-one-out density estimator; Pivotalness; 62G07; 62G10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-024-01655-w

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